We love this combination of dark-hued fruits, but you can swap in other berries, such as raspberries, or stone fruit, such as nectarines or peaches.
Make the biscuits: Preheat oven to 450 degrees. In a large bowl, whisk together flour, baking powder, salt, and 1 tablespoon sugar. Add 1 1/4 cups cream, and mix just until moistened.
Turn dough onto a floured surface, and pat into a 3/4-inch-thick round. Using a 3-inch biscuit cutter, cut 6 rounds (reuse scraps); transfer to a baking sheet. Brush tops with remaining 2 tablespoons cream, and sprinkle with remaining 2 tablespoons sugar. Bake until golden, 15 to 20 minutes; transfer to a wire rack to cool.
Make the filling: In a large bowl, combine plums, blackberries, 1/4 cup sugar, and salt. Squeeze grated ginger over fruit, releasing juice; discard pulp. Toss gently to combine. Let sit at least 15 minutes and up to 1 hour.
Just before serving, in a large bowl, whip cream and remaining 2 tablespoons sugar until soft peaks form.
With a serrated knife, halve biscuits horizontally. Place bottom half of each biscuit, cut side up, on a serving plate; top with fruit, whipped cream, and biscuit tops.